Mid-ocean ridges and geotherm distribution during mantle convection

Abstract

A boundary-layer solution for steady cellular convection is applied to thermal convection within the earth's mantle. For the large Prandtl and Rayleigh numbers applicable for the mantle, each cell contains a highly viscous core, on the horizontal boundaries of the cell are thin thermal boundary layers, and on the vertical boundaries between cells thin thermal plumes drive the viscous flow. Temperature and velocity distributions applicable to the mantle are obtained. With accepted values of the Rayleigh number the theory predicts a reasonable velocity for continental drift. Predicted values for the surface heat flux are in good agreement with measurements made on the ocean floors. The thickness of the thermal boundary layer adjacent to the earth's surface varies from about 8 km in the vicinity of the vertical rise to about 60 km near the descending plume. The vertical rise has a width of about 300 km with a similar width for the descending plume. In deriving the conditions for incipient upper mantle melting from experimental data on the melting of basalt, it is shown that in the upper part of an ascending plume the mantle is likely to undergo partial melting over an extensive mushroom-shaped area having a maximum width of about 400 km and extending to within 10 km of the surface. It appears that in the ascending plume mantle material may begin to melt over a range of temperature and pressure conditions that permit the development of a range of basaltic magma types. Thermal arguments are presented against serpentinite and in favor of basalt as the main constituent of layer 3 of the oceanic crust. The shape and characteristics of the zone of fusion suggest an explanation for the anomalous gravity and seismic observations associated with mid-oceanic ridges.